The present invention relates to the art of image processing. It finds particular application in conjunction with image enhancement, image smoothing, image zooming and other image improvement techniques for magnetic resonance images and will be described with particular reference thereto. It is to be appreciated, however, that the present invention is also applicable to enhancing, improving and enlarging digital x-ray images, computed tomographic images, nuclear camera images, positron emission scanners, and the like.
Medical diagnostic images have commonly been subject to image degradation from noise, system imperfections, and the like. Various image processing techniques have been utilized to remove the effects of the noise and to highlight some specified features. See for example "Digital Image Enhancement: A Survey" Wang, et al., Computer Vision, Graphics, and Image Processing, Vol. 24, pages 363-381 (1983). In one technique, each pixel was adjusted in accordance with the mean of surrounding pixels and the variation or difference between the pixel value and the local mean (the average of the surrounding pixels). The enhanced pixel value g'(i,j) was a weighted average of the local mean and the variation: EQU g'(i,j)=g(i,j)+k[g(i,j)-g(i,j)] (1),
where g(i,j) was the local mean, g(i,j)-g(i,j) was the variation, and k was a constant that weighted the relative contributions therebetween. It is to be appreciated that when k was set larger than 1, the variation, hence the fine details were magnified. As k was set smaller, the image was smoothed or blurred as if acted upon by a low-pass filter. At the extreme at which k was set equal to zero, each pixel value was replaced by the local mean of the neighboring pixel values.
One of the drawbacks in this technique resided in selecting an appropriate value for the weighting factor k. The smaller k was set, the more the image was blurred and the more difficult it became to extract accurate diagnostic information. As k was set larger, edges and fine details, including noise, became enhanced. Frequently, in a medical image, the selected weighting factor k was too large for some regions and too small for other regions.
"Digital Image Enhancement and Noise Filtering by Use of Local Statistics" by J. S. Lee, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 2, pages 165-168 (1980), recognized that different weighting factor k could be selected for each pixel to be enhanced. Specifically, Lee suggested setting the k for each pixel equal to the square root of the ratio of a preselected desirable local variance to the actual local variance of the selected pixel. Although Lee's weighting factor achieved better resultant images than the constant weighting factor, there was still room for improvement.
Another problem with medical diagnostic images resided in the blurring of enlarged or zoomed images. Typically, the diagnostic image included a fixed number of pixel values, e.g. a 256.times.256 pixel value matrix or array. When the image or a pattern thereof was enlarged each pixel could be displayed as a larger rectangle or additional intervening pixel values must be generated. For example, when a 256.times.256 array was enlarged to a 512.times.512 array, no data existed for alternate lines and for alternate columns of the 512.times.512 matrix. Commonly, the missing matrix values were interpolated by linear averaging the nearest neighboring pixel values. However, averaging adjacent pixels tended to blur the resultant enlarged image.
Another interpolation technique for zooming is described in "Analysis and Interpretation of Angiographic Images by Use of Fractals", T. Lundahl, et al., IEEE Computer in Cardiology, page 355-358 (1985). In Lundahl's technique, a global or image wide fractal model was utilized to derive the missing, intervening pixel values of an enlarged digital angiographic image. Lundahl, et al. first calculated a global fractal dimension for the entire image which described the average roughness or smoothness of the intensity surface of the entire image. The interpolated pixel values were based on the average of neighboring pixel values plus or minus a function of global fractal dimension. The plus or minus sign was chosen at random. One of the drawbacks in their technique is that the interpolated value was always different from the neighboring average by a function of the global fractal dimension when in fact, in the real world there is a certain chance for the interpolated value to be equal to the average of the neighboring values. While the addition or subtraction of a function of the global fractal dimension value made the image more realistic and easier to view, the interpolated pixel values were inaccurate and could cause an erroneous diagnosis. Particularly in low pixel value regions of an image with a large global fractal dimension, fictious image details could be generated during enlargement. This was caused by their use of the global fractal dimension in doing local interpolation. This is the other drawback of their technique.
The present invention is based on a new image fractal model, which describes images much more like real-world images. By the use of the fractal model, the processed medical image looks much more natural than the one by the use of traditional techniques.
The fractal model is based on the theory of fractal brownian motions developed by B. Mandelbrot. This theory provided a useful model for description of real-world surface. See `Fractal: Form, Chance, and Dimension` and `The Fractal Geometry of Nature`, B. Mandrelbrot, W. H. Freeman and Company (1977) and (1982) respectively.